Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι → ι → ι be given.

Let x3 of type ι → ι → ι be given.

Apply unpack_b_o_eq with λ x4 . λ x5 : ι → ι → ι . and (and (pack_b x0 x2 = pack_b x4 x3) (Group (pack_b x4 x3))) (x4 ⊆ x1), x0, x2.

Let x4 of type ι → ι → ι be given.

Assume H0: ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ x2 x5 x6 = x4 x5 x6.

Let x5 of type ο → ο → ο be given.

Assume H1: x5 (and (and (pack_b x0 x2 = pack_b x0 x3) (Group (pack_b x0 x3))) (x0 ⊆ x1)) (and (and (pack_b x0 x2 = pack_b x0 x3) (Group (pack_b x0 x3))) (x0 ⊆ x1)).

The subproof is completed by applying H1.

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Proofgold Proof